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Lecture notes Elementary Mathematics 1 (MAT111)

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Course
Elementary Mathematics 1 (MAT111)

Institution
Southwestern University

This course is the first course at the undergraduate level, designed primarily for students in mathematics, pure and applied sciences. However, it also meets the need of students in other fields. The course’s focus is to impart useful skills on the students in order to enhance their knowledge in ...

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Uploaded on July 4, 2022
Number of pages 28
Written in 2021/2022
Type Class notes
Professor(s) Daniel deborah
Contains All classes

number system
indices and logarithm
surds
mathematical induction
set

Institution
Southwestern University
Course
Elementary Mathematics 1 (MAT111)

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SOUTHWESTERN UNIVERSITY, NIGERIA

MAT 111 – ELEMENTARY MATHEMATICS I

Lecture Note by DANIEL Deborah O.

COURSE OUTLINE

 Number Systems
 Indices and Logarithms
 Surds
 Mathematical Induction
 Elementary Set Theory
 Equations
 Series and Sequences
 Partial Fractions
 Binomial Theorem and Binomial Series
 Complex Numbers

,NUMBER SYSTEM

Natural number are the counting numbers 1, 2, 3, 4,…

 {1, 2,3, }

Whole numbers include the natural numbers plus zero. Natural numbers are closed under the
operations of addition and multiplication only.
Integer: This is a set of numbers consisting of positive numbers, zero and negative numbers
(additive inverses of each natural numbers). It is denoted by . The operations of addition,
multiplication and subtraction are closed in the set of integers.
Rational numbers: These are set of number that consist of numbers that can be expressed in ratio
a
i.e where b  0 e.g 1/3, 11/7. Obviously, all integers are included in the set of of rational
b
number e.g 3.33=10/3. The set of rational number is denoted by . All the four basic
operations are closed in a set of rational numbers except the case case where we divide by
0 which is undefined.
Irrational numbers: These are numbers that cannot be expressed in ratios. In decimal form,
irrational numbers do not repeat or never end. Examples include  , e, 2 etc. Irrational
c
numbers are denoted by . Irrational numbers are divided into two parts Algebraic and
transcendental numbers. Algebraic numbers are solutions of some polynomial equation
while transcendental numbers are not.
Real numbers: This is a set of numbers containing rational numbers and irrational numbers. It
complete the number line. i.e  c
 . They are denoted by .
Complex numbers: This a set of numbers containing the real part and the imaginary part i.e a  bi
Hence,

 0   

, INDICES AND LOGARITHMS
Indices is the power or exponent which is raised to a number or a variable.
Laws of indices
 Addition law: x a  x b  x a b
xa
 Subtraction law: x a  x b   x a b
xb
 Multiplication law: ( x a ) b  x ab
1
 Negative law: x  a 
xa
 Zero law: x 0  1
a

 Law of fractional Index: x  b x a or ( b x ) a
b

Exercise
1) Simplify the following
a. 52  54
1 1
b. 49 2  7 0  7 2
c. 0.00013
1
d. 40 x 2  8 x
e. 10 x  0.00001
1
f. 3x 
81
4
g.  64 x
2x
2) Solve the exponential equation
a. 52 x  26(5) x  25  0

b. 32 x  4(3x1 )  27  0

c. 2 2 x  2 x1  8  0
d. 2 2 x 1  9(2 x )  4  0

e. 2 x 1  13(2 x )  4  0

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